
Notes on the Atiyah-Singer Index Theorem
by Liviu I. Nicolaescu
Publisher: University of Notre Dame 2005
Number of pages: 135
Description:
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
Download or read it online for free here:
Download link
(860KB, PDF)
Similar books
Triangles, Rotation, a Theorem and the Jackpotby Dave Auckly - arXiv
This paper introduced undergraduates to the Atiyah-Singer index theorem. It includes a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
(10815 views)
Projective and Polar Spacesby Peter J. Cameron - Queen Mary College
The author is concerned with the geometry of incidence of points and lines, over an arbitrary field, and unencumbered by metrics or continuity (or even betweenness). The treatment of these themes blends the descriptive with the axiomatic.
(14622 views)
Introduction to Evolution Equations in Geometryby Bianca Santoro - arXiv
The author aimed at providing a first introduction to the main general ideas on the study of the Ricci flow, as well as guiding the reader through the steps of Kaehler geometry for the understanding of the complex version of the Ricci flow.
(12266 views)
Natural Operations in Differential Geometryby Ivan Kolar, Peter W. Michor, Jan Slovak - Springer
A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.
(18890 views)